
Sampling from \( Q_{0} \)  can be significantly easier than sampling from \( Q_{t} \)  when approximating the expectation. The same convenience applies for conditional expectations over \( q_{t}(x \mid a) \)  (details in Appendix). Efficient evaluation of the aformentioned expectations are important in both fairness and training, i.e., evaluating subgroup risks [1]} and the cross entropy losses for \( c_{t} \) .
